London (CNN) -- A nurse at the hospital that was duped by a prank call from two Australian radio DJs concerning Prince William's pregnant wife, Catherine, has apparently committed suicide, the hospital confirmed Friday.

The nurse "was recently the victim of a hoax call," King Edward VII Hospital said in a media statement.

The DJs impersonated Queen Elizabeth II and Prince Charles in the prank call, in which some details of the Duchess of Cambridge's condition and care were given.

The nurse who died was the person who first took the hoax call and transferred it through to Catherine's ward, the hospital's public relations company said.

The hospital named her as Jacintha Saldanha and said she had worked there for more than four years as an "excellent nurse," who was well respected by co-workers.

The hospital "had been supporting her throughout this difficult time," the statement said.

The Duchess of Cambridge was discharged from the hospital Thursday after treatment for acute morning sickness.

A St. James's Palace spokesman said: "The Duke and Duchess of Cambridge are deeply saddened to learn of the death of Jacintha Saldanha.

"Their Royal Highnesses were looked after so wonderfully well at all times by everybody at King Edward VII Hospital, and their thoughts and prayers are with Jacintha Saldanha's family, friends and colleagues at this very sad time."

Separately, a palace spokesman told CNN: "At no point did the palace complain to the hospital about the incident. On the contrary, we offered our full and heartfelt support to the nurses involved and hospital staff at all times."

The hospital's chief executive, John Lofthouse, said, "Everyone is shocked by the loss of a much loved and valued colleague."

London's Metropolitan Police said they were notified around 9:35 a.m. (4:35 a.m. ET) on Friday that a woman was found unconscious. She was pronounced dead at the scene.

Police are treating the death as "unexplained," they said.

Audio of the call posted online suggested a woman spoke briefly to the DJs, who host a show for the 2Day FM radio station in Sydney, before the call was put through to the ward early Tuesday morning.

The hospital said Wednesday that it deeply regretted the call had been put through.

The radio show apologized for the call Wednesday, saying it "was done with light-hearted intentions."

Its two DJs, Mel Greig and Michael Christian, continued to tweet about the call on Thursday and earlier Friday, promising "more on the #royalprank." By Friday evening, a spokeswoman for the station told CNN in a statement that the pair will "not return to the show until further notice out of respect for what can only be described as a tragedy." She said Greig and Christian were "deeply shocked" by the incident.

The Twitter accounts for the pair were taken down.

Talking about the call on air Thursday, Greig said: "They were the world's worst accents ever. We were sure 100 people at least before us would've tried the same thing. ... We were expecting to be hung up on -- we didn't even know what to say when we got through."

Angry comments have been posted on the 2Day FM Facebook page since the news of the nurse's death broke.

"This death is on your conscience," reads one post. Another says, "Blood on your hands."